Fuse Blows on Bedroom Light Circuit

As far as measuring with your multimeter. Remember that a standard light bulb is nothing more than a relatively low resistance wire (the filament) connecting hot to ground. Two bulbs in parallel would measure half that resistance. Three = one third. Etc. So you will measure some continuity to ground from the hot wire with the bulbs still in the sockets. To check for no continuity you need to remove all bulbs in that circuit.